ETH/BTC is a symbol showing the price of Ethereum (ETH) against Bitcoin (BTC), the most popular cryptocurrency out there, i.e. how much Bitcoin you need to buy one Ethereum.
Ethereum, or Ether, is the second most popular cryptocurrency by capitalization. Basically, Ethereum is the name for a blockchain platform, so the currency is more often called Ether. The platform was first created in 2013, but it was only in 2015 when it started working. Its creator's name is Vitalik Buterin, who is a Russian-Canadian software developer.
Bitcoin is the most famous and widespread cryptocurrency known to date. It was first issued in 2009. Its overall capitalization has recently reached $150 Billion, which makes this digital currency an attractive investment vehicle.
With Bitcoin growing faster than Ethereum, ETH/BTC will be going down. Conversely, if the Ethereum price grows faster than Bitcoin, ETH/BTC will be rising.